Dynamic response of a visco-elastic half-space subjected to buried moving loads

The attenuation of the vibration of a three-dimensional visco-elastic half-space subjected to the embedded moving loads is investigated theoretically. By employing the Fourier integral transform method and the Helmholtz decomposition, the Navier equations for the ideal elastic medium are solved, and the dynamic components in the transformed domain are derived in the Cartesian coordinate. Combined with the boundary conditions and continuity conditions, the analytical solutions to the dynamic response of the viscoelastic half-space due to the embedded moving loads are obtained. When the depth of the moving loads is zero, the results obtained in this study are in good agreement with the published ones. By employing the IFFT method, some numerical examples are selected to discuss the influences of the depth, velocity and viscous damping of the soil on the propagation of the vibration and the amplitude spectra of the displacement.